A case of 'task-switching acalculia'

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

The neuronal code for number

Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions.

Examining the relationship between fatigue and cognition after stroke: A systematic review

Many stroke survivors experience fatigue, which is associated with a variety of factors including cognitive impairment. A few studies have examined the relationship between fatigue and cognition and have obtained conflicting results. The aim of the current study was to review the literature on the relationship between fatigue and cognition post-stroke. The following databases were searched: EMBASE (1980-February, 2014), PsycInfo (1806-February, 2014), CINAHL (1937-February, 2014), MEDLINE (1946-February, 2014), Ethos (1600-February, 2014) and DART (1999-February, 2014). Reference lists of relevant papers were screened and the citation indices of the included papers were searched using Web of Science. Studies were considered if they were on adult stroke patients and assessed the following: fatigue with quantitative measurements (≥ 3 response categories), cognition using objective measurements, and the relationship between fatigue and cognition. Overall, 413 papers were identified, of which 11 were included. Four studies found significant correlations between fatigue and memory, attention, speed of information processing and reading speed (r = -.36 to .46) whereas seven studies did not. Most studies had limitations; quality scores ranged from 9 to 14 on the Critical Appraisal Skills Programme Checklists. There was insufficient evidence to support or refute a relationship between fatigue and cognition post-stroke. More robust studies are needed.

An integrative view of Luria's perspective on arithmetic problem solving: the two sides of environmental dependency

INTRODUCTION

A. R. Luria was the first author to hypothesize that executive dysfunction can lead to specific deficits in arithmetic problem solving, showing that patients' performance depends on the structure of the tasks. Cummings (1995. Anatomic and behavioral aspects of frontal-subcortical circuits. Annals of the New York Academy of Sciences, 15, 1-13) proposed the term "environmental dependency" to define such behavioral disorders triggered by the characteristics of the test and pointed out also the role of executive impairments. Few studies compare executive functioning and problem solving in brain-damaged patients, and none have examined the question from this point of view. Thus, the main aim of the present paper was to study the relationship between environmental dependency and executive functions.

METHOD

Fifty neurological patients with frontal, subcortical, and posterior brain lesions were compared to 45 matched healthy controls and were divided into two groups (dysexecutive/nondysexecutive) according to their performances on executive tasks. Then, we confronted the results of the two groups on an experimental protocol designed in accordance with Luria's proposals. We made also comparisons between groups on the basis of lesion location.

RESULTS

Our findings indicate a high association between executive functions and environmental dependency, showing that dysexecutive patients' performances were dependent on task demands. In addition, a specific frontal behavior not associated with executive functions and characterized by the solving of insoluble problems was highlighted.

CONCLUSION

The discussion focused on the interest to take into account the methodological and clinical contributions of environmental dependency. Based on our findings and theoretical arguments, we highlight the need to fractionate this concept.

On the dependency of division on multiplication: selective loss for conceptual knowledge of multiplication

This study reports the case of a patient (AG) whose main calculation problem was with multiplication that was severely affected at all levels including that of conceptual knowledge. In contrast AG's problems with addition, subtraction and division were much less conspicuous and just involved the use of procedures. For all these latter operations, and for division in particular, conceptual knowledge was spared. Despite his procedural problems, AG in fact was fully aware that division consists of finding out how many times a given quantity is contained in another quantity. Thus while he was able to reach the correct results for division by subtracting the divisor from the dividend, he never used the reverse strategy to complete multiplication operations, i.e. add the number for as many times as the multiplier to complete the operation, and showed no awareness that this was what multiplying means, even when explicit suggestions were made by the examiner. The existence of AG's case could not be expected on the basis of theories holding that division depends on multiplication and that is not separately represented in semantic memory. It follows, therefore, that the extent to which division depends on multiplication needs to be reconsidered.